A282058 Numbers that are not triangular numbers and cannot be written as the sum of a triangular number and two odd squares.

4, 7, 9, 14, 22, 42, 43, 48, 52, 67, 69, 72, 87, 114, 144, 157, 159, 169, 357, 402, 489, 507, 939, 952, 1029

Offset

1,1

Comments

The sequence is conjectured to be complete (cf. Sun, 2009, Conjecture 1.2 (ii)).

Links

Table of n, a(n) for n=1..25.

Zhi-Wei Sun, On sums of primes and triangular numbers, Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2009), 65-76 (Article 6), [arXiv:0803.3737 [math.NT], 2009].

Prog

(PARI) list(lim)=my(v=List(), u=vectorsmall(lim\=1), s, t); forstep(a=1, sqrtint(lim), 2, my(a2=a^2); forstep(b=1, min(sqrtint(lim-a2), a), 2, t=a2+b^2; my(k=0); while((s=t+k*(k+1)/2)<=lim, u[s]=1; k++))); t=1; while((s=t*(t+1)/2)<=lim, u[s]=1; t++); for(i=1, lim, if(u[i]==0, listput(v, i))); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017

Crossrefs

Cf. A000217, A016754, A141273.

Sequence in context: A310966 A287559 A032778 * A210497 A010383 A010403

Adjacent sequences: A282055 A282056 A282057 * A282059 A282060 A282061

Keyword

nonn

Author

Felix Fröhlich, Feb 05 2017

Status

approved